$f(n) = 6n^{2}-2(g(n))$ $g(n) = 4n^{2}-4n$ $ g(f(2)) = {?} $
Answer: First, let's solve for the value of the inner function, $f(2)$ . Then we'll know what to plug into the outer function. $f(2) = 6(2^{2})-2(g(2))$ To solve for the value of $f$ , we need to solve for the value of $g(2)$ $g(2) = 4(2^{2})+(-4)(2)$ $g(2) = 8$ That means $f(2) = 6(2^{2})+(-2)(8)$ $f(2) = 8$ Now we know that $f(2) = 8$ . Let's solve for $g(f(2))$ , which is $g(8)$ $g(8) = 4(8^{2})+(-4)(8)$ $g(8) = 224$